A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data. (a) Assume all conditions for inference are met. Construct and interpret a 95 percent confidence interval for the slope of the least-squares regression line. (b) Does the confidence interval contradict the agent’s belief about the relationship between selling price and distance from the city center? Justify your answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 16HP
icon
Related questions
Question
100%

A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data.

(a) Assume all conditions for inference are met. Construct and interpret a 95 percent confidence interval for the slope of the least-squares regression line.

(b) Does the confidence interval contradict the agent’s belief about the relationship between selling price and distance from the city center? Justify your answer.

 

$310
$300-
$290-
$280 -
$270
$260 -
$250
10
15
20
25
Distance from City Center (miles)
Predictor
Coef
SE Coef
т
P
Constant
301.7
1.80
167.17
0.000
Distance
-2.158
0.149
-14.45
0.000
S-4.4336
R-sq - 92.1%
Selling Price (thousands)
Transcribed Image Text:$310 $300- $290- $280 - $270 $260 - $250 10 15 20 25 Distance from City Center (miles) Predictor Coef SE Coef т P Constant 301.7 1.80 167.17 0.000 Distance -2.158 0.149 -14.45 0.000 S-4.4336 R-sq - 92.1% Selling Price (thousands)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage